What an irrational equation is

An equation is called irrational when the unknown appears under the radical sign. To solve it, one isolates the root and squares; this step, however, can introduce “false” solutions that must be eliminated by checking.

Example — How to invent an equation with $x$ under a root

1. Write an identity between two numbers that are perfect squares, e.g. $9=9$.
2. Take the root: $\sqrt{9}=3$.
3. Decide the result, e.g. $x=8$.
4. Write $9$ as an expression involving $8$, e.g. $x+1=9$.
5. The equation is $\sqrt{x+1}=3$, with solution $x=8$.

Links

Topics: Radicals
Concepts: Irrational equation
Skills: Solving equations